Drug Infusions - calculating hourly rates

Being asked to write up your first morphine or dopamine infusion in neonatal intensive care looks like a challenge.  Actually it is not so bad.  You just have to work out the hourly rate.  Look at these equations below and remember you need to work in the same units in your calculations, so for example don't forget to convert your milligrams to micrograms or your minutes to hours!

1a) Micrograms per kilograms per minute to ml/hr

ml/hr =  dose required in mcg/kg/min x weight (kg) x 60

                  concentration of solution in mcg/ml

Example:

Baby A weighs 1.490 kg and has been prescribed an infusion of dopamine to be run at 1 micrograms/kg/min.  The solution prescribed is 40mg dopamine in 50mls.  What rate should the pump be set to run at

1 x 1.49 x 60   =   89.4 = 0.11mls/hr

40000/50              800

1b) To check the rate in micrograms/kg/min of an infusion already running:

Infusion rate (ml/hr) x concentration of solution (mcg/ml) = mcg/kg/min

                  weight x 60

2a) Micrograms per kg per hour to ml/hr

ml/hr =  dose required in mcg/kg/hr x weight (kg)

                  concentration of solution in mcg/ml 

2b) To check the rate in micrograms/kg/hour of an infusion already running:

Infusion rate (ml/hr) x concentration of solution (mcg/ml) = mcg/kg/hour

                                 weight

Working with drug infusions where solution concentration is made up proportional to the patient's weight

The advantage of this approach is that the rate in ml/hr will be the same regardless of patient weight as long as you use the same volume of solution to add the drug to (eg 1mg/kg of morphine in 50ml of 10% dextrose = 20 micrograms/kg/ml).

3a) Micrograms/kg/hour to ml/hr*


rate in ml/hr = dose required in micgrograms/kg/hr
                      concentration in micrograms/kg/ml

4a) Micrograms/kg/min to ml/hr:

ml/hr =  dose required in mcg/kg/min  x 60      

             concentration of solution in mcg/kg/ml

* If you want to know how the above equation in 3a is derived:

eg for a morphine infusion, say the guideline says make up 1mg/kg of morphine in 50ml of solution and run at 

10 micrograms per kilogram per hour

1mg/kg of morphine in 50ml of solution = 0.02 mg/kg/ml = 20 micrograms/kg/ml

using equation 2a above (noting that we have to multiply the above concentration by weight in the denominator to get the actual concentration) :

rate ml/hr =     10 mcg/kg/hour x weight = 10 = 0.5 ml/hr
                       20 mcg/kg/ml x weight       20

As you can see you can cancel out the weights, getting the equation above

Further Resources

Maths for medics